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%I #28 Jan 01 2023 09:44:29
%S 2,2,6,2,3,5,7,3,4,3,6,93,2,88,5,33,5,196,15,106,174,196,14,342,207,
%T 28,372,14,47,25,569,646,141,129,278,5,421,224,629,26,424,1081,688,
%U 246,736,4392,124,484,759,791,4401,863,2854,410,1044,22,848,1402,2006
%N Least positive integer m > 1 such that 1 - m^k + m^(2*k) is prime, where k=A003586(n).
%C 1 - m^k + m^(2*k) equals Phi(6*k,m) when k=2^p*3^q, p>=0, q>=0, which may be prime numbers for certain positive integer m>1.
%C The Mathematica program given here generates the first 33 terms. Further terms were generated by OpenPFGW.
%C a(62)=7426, while A003586(62)=3^8=6561.
%F a(n) = A085398(6*A003586(n)). - _Jinyuan Wang_, Jan 01 2023
%e n=1, A003586(1)=1, when m=2, 1-2^1+2^2=3 is prime, so a(1)=2;
%e n=2, A003586(2)=2, when m=2, 1-2^2+2^4=13 is prime, so a(2)=2;
%e ...
%e n=7, A003586(7)=9, when m=7, 1-7^9+7^18=1628413557556843 is prime, so a(7)=7.
%t fQ[n_] := n == 3 EulerPhi@n; a = Select[6 Range@500, fQ]/6; l =
%t Length[a]; Table[m = a[[j]]; i = 1;
%t While[i++; cp = 1 - i^m + i^(2*m); ! PrimeQ[cp]]; i, {j, 1, l}]
%Y Cf. A003586, A056993, A085398, A153438.
%K nonn,hard
%O 1,1
%A _Lei Zhou_, Feb 01 2012
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